Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method

He's homotopy perturbation method for solving Korteweg‐de Vries Burgers equation with initial condition

“…Chowdhury and Hashim obtained approximate and exact analytical solutions of the generalized Emden-Fowler type equations in the second order ordinary differential equations (ODEs) by homotopy-perturbation method (HPM) in [45]. The two-dimensional KdV-Burgers equation is solved by Molabahrami et al [46] by using HPM. Zhang et al [47] solved the modified Camassa-Holm and Degasperis-Procesi equations by the HPM.…”

Application of Extended Tanh Method to Generalized Burgers-type Equations

“…This equation is model equation for wide class of nonlinear wave models of fluid in an elastic tube, liquid with small bubbles and turbulence [14,16,28,30,36]. It has been considered to find out its exact solution by some analytic methods [11,22,35]. In this section, we employ the extended tanh method to find soliton solutions of the generalized two-dimensional Burgers-KdV equation.…”

Analytic study on two nonlinear evolution equations by using the (G′/G)-expansion method

“…A second instructive model is the following 2D-KdVB equation in the form: [14][15][16][17][18][19][20] and references therein. Letting u(x, y, t) = U(n), n = x + ly À ct in Eq.…”

“…Elcin [13] studied the mCH equation using the Exp-function method and revealed new solutions. There are many studies for the 2D-KdVB equation, and some profound results have been established by the authors [14][15][16][17][18][19][20] using the well-known techniques; the extended tanh method, the homotopy perturbation method, the Adomian decomposition method, the first integral method, etc.…”